Graceful Labeling of Bow Graphs and Shell-Flower Graphs
Jeba J. Jesintha · International Journal of Computing Algorithm · 2013
A graceful labeling of a graph G with ‘q’ edges and vertex set V is an injection f: VG → {0,1,2,….q} with the property that the resulting edge labels are also distinct, where an edge incident with vertices u and v is assigned the label |fu – fv| . A graph which admits a graceful labeling is called a graceful graph. A Shell graph is defined as a cycle Cnwith n -3 chords sharing a common end point called the apex . Shell graphs are denoted as Cn, n- 3. A multiple shell is defined to be a collection of edge disjoint shells that have their apex in common. Hence a double shell consists of two edge disjoint shells with a common apex.